Olha Silina

activity

20242026

collaborators

5 papers

math.CO2026

Lattice Structure and Efficient Basis Construction for Strongly Connected Orientations

Siyue Liu, Olha Silina

Let $G = (V, E^{+} \cup E^{-})$ be a bidirected graph whose underlying undirected graph $G = (V, E)$ is $2$ -edge-connected. A strongly connected orientation (SCO) is defined as a subset…

math.CO2026

Integral bases, perfect matchings, and the Petersen graph

Ahmad Abdi, Olha Silina

Let $G = (V, E)$ be a matching-covered graph, denote by $P$ its perfect matching polytope, and by $L$ the integer lattice generated by the integral points in $P$ . In this paper, we gi…

math.CO2026

Strongly connected orientations and integer lattices

Ahmad Abdi, GÃ©rard CornuÃ©jols, Siyue Liu +1

Let $D = (V, A)$ be a digraph whose underlying undirected graph is $2$ -edge-connected, and let $P$ be the polytope whose vertices are the incidence vectors of arc sets whose reversal…

math.CO2025

A Polyhedral Perspective on the Perfect Matching Lattice

Olha Silina

We study the perfect matching lattice of a matching covered graph $G$ , generated by the incidence vectors of its perfect matchings. Building on results of LovÃ¡sz and de Carvalho,…

math.CO2024

Covering the edges of a graph with perfect matchings

Olha Silina

An $r$ -graph is an $r$ -regular graph with no odd cut of size less than $r$ . A well-celebrated result due to LovÃ¡sz says that for such graphs the linear system $A x = 1$ ha…